The direction co-sines of the line which bisects the angle between positive direction of $Y$ and $Z$ axes are

The direction co-sines of the line which bisects the angle between positive direction of $Y$ and $Z$ axes are
  1. $\frac{1}{\sqrt{2}}, 0, \frac{1}{\sqrt{2}}$
  2. $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, 0$
  3. $0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$
  4. $\frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}$

Solution

Vector parallel to bisector of angle between positive $\mathrm{Y}$ and $\mathrm{Z}$ direction. $=\hat{\mathrm{j}}+\hat{\mathrm{k}}$ and its magnitude is $\sqrt{1+1}=\sqrt{2}$ $\therefore$ Direction cosines $=\left(0, \frac{1}{\sqrt{2}}, \frac{1}{\sqrt{2}}\right)$

Asked in: MHT CET 2020 (16 Oct Shift 2)

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